Children born in the covenant (or sealed later):
Joseph Fielding Smith:
From Robert Millet's book "When a Child Wanders."
 Quoting Lorenzo Snow:
A Word For The Wayward

Orson F. Whitney, Conference Report, April 1929, p.110
A Precious Promise
May 1992 Ensign, pg. 68 by Elder Packer:
Orson R. Whitney, quoting the prophet Joseph Smith:

    "The Prophet Joseph Smith declared--and he never taught more comforting doctrine--that the eternal sealings of faithful parents and the divine promises made to them for valiant service in the Cause of Truth, would save not only themselves, but likewise their posterity.  Though some of the sheep may wander, the eye of the Shepherd is upon them, and sooner or later they will feel the tentacles of Divine Providence reaching out after them and drawing them back to the fold.  Either in this life or the life to come, they will return.  They will have to pay their debt to justice; they will suffer for their sins; and may tread a thorny path; but if it leads them at last, like the penitent Prodigal, to a loving and forgiving father's heart and home, the painful experience will not have been in vain.  Pray for your careless and disobedient children; hold on to them with your faith.  Hope on, trust on, till you see the salvation of God."   (Orson F. Whitney, CR Apr. 1929, pg. 110.)

    "We cannot overemphasize the value of temple marriage, the binding tie of the sealing ordinance, and the standards of worthiness required of them.  When parents keep the covenants they have made at the altar of the temple, their children will be forever bound to them, President Brigham Young said:
'Let the father and mother, who are members of this Church and Kingdom, take a righteous course, and strive with all their migh never to do a wrong, but to do good all their lives; if they have one child or one hundred children, if they conduct themselves towards them as they should, binding them to the Lord by their faith and prayers, I care not where those children go, they are bound up to their parents by an everlasting tie, and no power of earth or hell can separate them from their parents in eternity; they will return again to the fountain from whence they sprang.'    (Discourse of Brigham Young, Compiled by John A. Widtsoe, pg. 208)"
James E. Faust, “The Greatest Challenge in the World—Good Parenting,” Ensign, Nov. 1990, 32


       
"Perhaps in this life we are not given to fully understand how enduring the sealing cords of righteous parents are to their children.  It may very well be that there are more helpful sources at work than we know.14 I believe there is a strong familial pull as the influence of beloved ancestors continues with us from the other side of the veil."

President James E. Faust, "Dear are the Sheep that have Wandered", May 2003 Ensign


"This principle has to do with the hope that Latter-day Saints have as they honor the sacred gospel covenants they made at the marriage altar in the temple. They and their children born or sealed in the covenant have a right to spiritual help in this life. Even those children who have for a time forsaken the gospel often speak of a recurring, troubling need to return to the fold. Perhaps these desires come to them because they are children of the covenant—children whose hearts, planted with patriarchal promises, “shall turn to their fathers.” (D&C 2:2.)

"What hope does the gospel give to parents of errant youth?" - Harold C. Brown, “I Have a Question,” Ensign, Mar. 1993, 53–54



    "Some parents suffer greatly because they blame themselves unduly for having been poor parents. In this position they are likely to misapply President David O. McKay’s wonderfully prophetic statement that “no other success can compensate for failure in the home” (in Conference Report, Apr. 1964, 5). They seem to draw the unintended implication that since they have a child who is abusing drugs or alcohol, they must be failures as parents; hence, no matter how hard they have tried, no other good they have done or success they have achieved can compensate for their parental failure at home. Because this statement was intended to inspire parents to become or stay involved with their children, it should not be taken to mean that parents who have indeed put great time, effort, and sacrifice into parenting, and yet who have still not reaped the desired rewards, have failed. A closer look at additional counsel and doctrines may provide much needed perspective."

John K. Carmack, “When Our Children Go Astray,” Ensign, Feb. 1997, 7